I honestly don't know where to begin...

First things first, Metal Gear Solid is a must, I also recommend Peace Walker, highly improved version of Portable Ops, though I'm not sure if it's available on PSN.

Both Parasite Eve games, second one in particular, survivor horror with RPG elements. Speaking of survivor horror, Silent Hill Origins is another great game I recommend.

Gran Turismo would be your best choice as far as racing games go, gorgeous graphics, realistic driving experience, well, more or less, and 800 cars just waiting to be driven.

I have yet to play Jak and Daxter: The Lost Frontier, Daxter on the other hand is one of the best platformers I've played, the very best on PsP, so if you're into it give it a try. Also, the old Crash Bandicoot, and Spyro games.

Tekken 5: Dark Resurection, BlazBlue Portable, and Soulcalibur: Broken Destiny, top of their genre, on PsP that is.

Vagrant Story, bit weird, but great RPG nevertheless. Final Fantasy IV: Complete Collection is also out, anniversary edition of first two Final Fantasy games would be worth getting as well...

...I'll edit this later, add bunch of more games, right now I need my sleep =).